Capture of photoexcited carriers in a single quantum ... - IEEE Xplore

lEEE

JOURNAL OF QUANTUM

ELECTRONICS, VOL 21

NO

6, JUNE 1991

I669

Capture of Photoexcited Carriers in a Single Quantum Well with Different Confinement Structures S. Morin, B. Deveaud, F. Clerot, K. Fujiwara, and K. Mitsunaga

Abstract-We report experimental and theoretical studies of photoexcited carrier trapping in a GaAs-Al,Ga, -,As single quantum well with three different typical confinement layer structures: standard separate-confinement heterostructure (SCH) or graded SCH (GRIN-SCH, linearly graded LGRINSCH, or parabolically graded PGRIN-SCH). The capture is studied by means of time-resolved luminescence with 600 fs resolution. Measurements, performed from 20 to 300 K, show an appreciably shorter trapping time in the GRIN-SCH (2 ps at 80 K to 8 ps at 300 K) than in the SCH (between 22 and 14 ps in the same temperature range). Experimental results are fitted by a one-dimensional “drift-diffusion” model, and the mobility of holes is deduced from the calculations. We evidence a short but finite capture time at the edge of the well. The diffusion process is limited by holes in the direct region of the alloy and by both particles in the indirect part of the confinement layer.

I. INTRODUCTION HE high-speed properties of many optoelectronic devices, and particularly semiconductor lasers, depend on the carrier trapping dynamics in a single quantum well (QW). In the case of QW lasers, the modulation frequency depends on different parameters such as differential gain or gain saturation, but a finite trapping time sets an upper limit to the modulation frequency. In a different way, this study is of great interest because the basic physical mechanisms involved are not yet well understood despite the large number of studies made on this topic. Trapping of carriers by a quantum well has been thoroughly studied experimentally, and different conclusions for the trapping efficiency have been drawn [1]-[5]. As far as theory is concerned, capture in a quantum well is now supposed to be mainly mediated by optical phonons, and there have been predictions of strong resonances in the capture time [6]-[9]. The theoretically estimated trapping times would oscillate from 1 to 200 ps as a function of the well width L,. Resonance effects resulting from variations in the confined phonon modes as a function of L, have been subsequently predicted [lo], and they might modify this picture to a great extent and blur out the oscillations, giving times on the order of a few picoseconds.

T

Manuscript received October 15, 1990; revised February 15, 1991. S. Morin, B . Deveaud, and F. Clerot are with the Centre National d’Etudes des TCl6communications (LAB/OCM), 2300 Lannion, France. K. Fujiwara was with the Mitsubishi Electric Corporation, Amagasaki, Hyogo 661, Japan He is now with A T R , Kyoto 619-02, Japan K Mitsunaga is with the Mitsubishi Electric Corporation, Amagasaki, Hyogo 66 1 , Japan IEEE Log Number 9100220.

Large differences are expected between GaAs quantum wells where phonons are confined and InGaAsP-InP where they are not. Time-resolved studies of the decay of the barrier luminescence, performed recently with subpicosecond resolution [3], [ l l ] , 1121, show that as loag as the barrier thickness is not too large (less than 200 A), the photoexcited carriers are trapped very quickly by the well. The measured times still vary, but only in the range 0.3-5 ps; part of the discrepancies might be due to high-density effects. In the case of narrow barriers, the capture process, which can in principle be modeled by a quantum mechanical description using the electron or hole wavefunctions, and treating the scattering process as a perturbation [6], [8] can be called “quantum capture.” The quantum capture time has been first estimated to be less than 300 fs for holes and less than 1 ps for electrons [3]. Recent experiments on multiple-quantum-well structures show that this capture time has been slightly underestimated [13], and it is found to range between 650 fs and 1.2 ps [ 141 in the case of GaAs-AlGaAs quantum wells when the barrier luminescence decay is directly measured at low densities. This is shorter than theoretical calculations, and moreover, these experimental times are found to be independent of the well width [ 151. A precise understanding of this discrepancy between theory and experiments has not yet been achieved. When the barrier thickness is larger than the mean free path of at least one of the carriers, one has to take into account the scattering of the carriers in the barriers. The capture is not only limited by the quantum capture process, but also by the diffusion in the confinement layers (CL’S). The “total capture time,” which includes the diffusion in the barrier and the quantum capture by the well, again can be measured by the decay of the luminescence arising from the confinement layer [6], [7], [16]. The performances of semiconductor lasers are improved in symmetric separate confinement heterostructure lasers by optimizing the layer structure [17], [18]. By using molecular beam epitaxy to grow the very thin active layer needed, low threshold currents and stable, narrow beam divergence are obtained [ 181. It has been proposed by Tsang 191 that improvements Of the quantum-well laser Derformances would be obtained with graded-index waveguide separate-confinement heterostructures (GRIN-SCH). In such structures, instead of the usual constant composition barrier, the confinement layer

0018-9197/91/0600-1669$01.00

0 1991 IEEE

I EEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 27, NO. 6, J U N E 1991

1670

gap varies from a smaller value at the edge of the well to a larger one at the end of the barrier. Compared to SCH, the GRIN-SCH structures offer three main advantages: 1) the graded-index waveguide allows us to vary the propagation characteristics and to control the far-field beam distribution, optical modes are Hermite-Gaussian, and a strong mode discrimination is obtained [ 191; 2) the threshold current is twice as small in separate confinement heterostructures [ 191; and 3 ) the coefficient To, which characterizes the threshold current temperature dependence, is higher than for classical structures [20]. Moreover, one might expect that the capture of carriers is speeded up by the built-in quasi-electric field due to the graded gap region. The GRIN-SCH structures should then allow higher frequency laser operation (i.e., faster modulation speed) than the SCH structures. In this paper, the influence of the confinement layer structure on the trapping time is studied comparatively for an SCH, a PGRIN-SCH (parabolic GRIN-SCH), and an LGRIN-SCH (linear GRIN-SCH) by the measurement of the CL luminescence decay time with subpicosecond resolution. We extend the experiments reported in [21] by varying the temperature up to 300 K. The dependence of the “overall capture time” and the mobility on temperature is investigated for each structure. We also perform a full analysis of the data with a drift-diffusion model. The paper is organized as follows: after this Introduction, Section I1 describes the experimental technique and the structures of our samples. In Section 111, comparative results of time-resolved luminescence experiments are discussed. Section IV presents the drift-diffusion model used to fit the experimental measurements. Section V describes the estimation of the mobility and the influence of the parameters of the model on the fit of experimental data. Finally, Section VI compares the SCH structure and the LGRIN-SCH structure in terms of velocity of the capture under the same initial carrier distribution. 11. EXPERIMENTAL DETAILS All samples have been grown by MBE (moleSular beam epitaxy) and have the same well width (50 A ) and the same confinement layer width (2000 on each side of the QW). The SCH is composed of a GaAs QW cladded by Alo,3Gao,7AsCL with outer barriers of Alo,6Gao4A~ (A1 contents are the nominal values). In the LGRIN-SCH, the aluminum concentration of the CL varies linearly from 30% at the edge of the well to 60% at the beginning of the outer barriers. In the PGRIN-SCH, aluminum concentration has been quadratically varied between the same values (Fig. 1). The samples are nominally undoped. These samples have already been studied by CW and picosecond luminescence [4], [ 161 and subpicosecond time-resolved luminescence at low temperature [2 11. Our PL and PLE measurements on the SCH structure confirm that the gap of the CL is at 1.85 eV (x = 0.27) and at 2.1 eV for the outer barrier (x = 0.6) which corresponds to the indirect gap. For Al,Ga, - ,As, the crossover of the X and Cvalleys occurs f o r x = 0.43 (2.05 eV at 20 K) [22]. Thus, the crossover point is in the graded-index region of

A

-

SCH

....-.

P-GRINSCH

_ _ L - G R I NSCH Fig. 1 . Bandgap profile of the three structures used for the experimental measurements (nominal values at T = 20 K).

A

the two GRIN-SCH structures: it is 1000 ayay from the well for the LGRIN-SCH, and at 1400 A for the PGRIN-SCH. Our excitation energy (2.04 eV) is larger than the gap of AlGaAs at the r-X crossover, but lower than the outer barrier bandgap. Up to the crossover position, photocarriers are created directly in the r valley; from this point and up to the position where the J? gap becomes larger than the excitation energy, photocarriers created in the r valley are transferred very quickly (about 100 fs) to the X valley (we neglect the number of electrons excited in the X valley be indirect absorption). They will then drift because of the quasi-electric field down to the crossover where they are transferred back to the I‘ valley. Note that the position of the crossover does not depend on the temperature. The samples are excited with 600 fs duration pulses generated by a synchronously pumped hybrid dye laser with a repetition rate of 80 MHz. Time-resolved luminescence measurements are performed with an up-conversion technique like the one described in [23]. With such as system, the experimental resolution is limited primarily by the pulse duration. 111. EXPERIMENTAL RESULTS Typical luminescence spectra of the LGRIN-SCH are shown on a semilog scale in Fig. 2 for two different delays after the pulse excitation. After 1 ps, three peaks are observed corresponding, respectively, to the GaAs buffer layer (1.5 eV), the well (1.6 eV), and the confinement layer (1.85 eV). Note that the energy of the CL luminescence roughly corresponds to the energy gap of the alloy at the edge of the well. After 10 ps, the luminescence of the CL has completely disappeared, while the intensity of the two other peaks has weakly increased. Disappearance of the CL luminescence is a result of the capture of at least one type of carrier. The increase of the two other peaks is due to the capture and thermalization of photoexcited carriers [24]. Thus, we are able to measure the “overall capture time” directly from the CL luminescence time behavior. In order to work at densities corresponding to laser action, experimental measurements are made with a 3 mW power excitation, which corresponds to an excitation density of 6 X lo’* cm-2. At this density, the well is filled with electrons, and some of them have to wait in the bar-

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MORIN er ol.: CAPTURE OF PHOTOEXCITED CARRIERS IN SQW

100

1

DELAY I p s 1

Fig. 4. Time dependence of the barrier luminescence at T SCH structure.

ENERGY I e V l

Fig. 2. Luminescence spectra of the LGRIN-SCH structure at T = 20 K and excitation density of 6 x 10l2 c t K 2 . Note that after 10 ps, the barrier luminescence had disappeared.

=

120 K for the

TABLE 1 DECAY TIME(PS) OF THE BARRIER LAYER FOR THE THREE STRUCTURES BETWEEN 20 AND 30 K Decay Time (ps) Temperature (K)

-1

DELAY I p s 1

15

Fig. 3. Time dependence of the barrier luminescence at T = 120 K for the LGRIN-SCH and the PGRIN-SCH structures.

rier before being captured; hence, what we observe, in fact, corresponds to the changes in the hole population at the edge of the well [21]. Fig. 3 shows a decay curve of the CL luminescence; after a rise at short times due both to the arrival of the carriers at the edge of the well and to their thermalization, we observe a very fast decay with a time constant of 2.3 ps at 120 K for the LGRIN-SCH; we must emphasize that we are not limited here by the experimental resolution, which is better than 1 ps. In the PGRIN-SCH, the time constant is a bit longer (3.5 ps); this is probably due to the lack of a quasi-electric field at the edge of the well since this sample has been made to have a constant composition at this point. We can also notice that, in the PGRIN-SCH, the absorbing zone at our laser energy extends further from the well. In the case of the SCH (Fig. 4), the “overall capture time” is dramatically longer (17 ps) because there is no built-in quasi-electric field (the CL is of constant composition). The observed decay times are given in Table I. The temperature has been varied from 20 to 300 K: graded structures are always faster than the SCH. IV. ESTIMATION OF THE DIFFUSION COEFFICIENT In the SCH structure, the CL thickness is much larger than the mean free path of the carriers in AlGaAs, so the quantum capture is not the main limiting factor, and the time response of the laser structure is given by the diffusion of the carriers in the CL. Hence, the behavior of the sample can be fitted to a one-dimensional diffusion model

1251. In the LGRIN-SCH structure, the carrier population experiences a high quasi-electric field; the characteristic time of the drift process in the CL is not long anymore compared to the quantum capture time. We shall, how-

20 80 120 150 190 220 250 300

SCH

LGRIN-SCH

PGRIN-SCH

I80 22 17 16

2 2 2.2 2.4 2.7

2.9 3 3.5 3.8 4.4 5.2 8.4

14

16 17.5 19.2

4.5

6.9 8.2

10

ever, also fit its temporal behavior to a classical “driftdiffusion” model. The evolution equation for the carrier population of the CL can then be written dnb(z)/dt = Damb(d2nb/dZ2- q / k T dE,/dZ *

d n d d z ) - nt,/q,

-f(z)

*

nb/7,.

where

z

is the direction perpendicular to the layers nb = nb(z, t ) is the areal carrier density in the CL Damb is the ambipolar mobility T is the temperature of the lattice is the electron charge q is the built-in quasi-electric field dE,/dz is the lifetime of carriers in the CL 7b is the finite quantum capture time 7, f ( z ) = 1 if z is within the capture area = 0 otherwise. As we use high densities, we assume an ambipolar diffusion of the carriers (see also [9]): in the SCH, the mobility is then approximately twice the hole mobility [ 2 6 ] . In the LGRIN-SCH, we have to account for the fact that, in the barrier layer, different valleys are affected by the transport. This leads, due to the low mobility in the X valley, to a ratio of ambipolar diffusion coefficients DambX/Dambr = 2 / 3 between the indirect and direct regions of the structure. We also assume that, above the crossover, all of the photocarriers created in the r valley are instantaneously transferred to the X valley. Obviously, this is the most unfavorable situation, and the effect probably will be overestimated. We take the usual band offset ratio of 35-65 % . Surface recombination is neglected, and the lifetime of the car-

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riers in the CL is supposed to be infinite compared to the “overall capture time. ” This assumption is valid above 80 K where the decay time due to the capture in the well (approximately 20 ps) is much shorter than the nonradiative lifetime in AlGaAs. The case of low-temperature experiments will be discussed separately below. We also consider that the temperature of the carriers is constant and equal to the lattice temperature. In order to account for the finite qyantum capture time, we allow the carriers less than 1.50 A from the well to be captured in a finite time (a similar assumption was made in [2.5]).The finite width of the pulse is also taken into account. Of course, the capture time and capture area are coupled parameters. In order to fit the data, we may increase the capture width and simultaneously increase the capture time. However, as we fit two different structures, $is cannot be done outside a typical range of 100-400 A for the capture area. Variations over this range correspond to variations of the capture time by slightly more than a factor of two. The value of 1.50 A is nevertheless quite reasonable for the mean free path of the holes in an AlGaAs barrier. Furthermore, we know from the low-temperature measurements, where we observe a decay time of only 2 ps, that the capture time cannot be larger than this value. Input parameters are the mobility, the quantum capture time, and the extension of the capture area on each side of the well. The diffusion coefficient is estimated from Einstein’s relation at the lattice temperature. We have plotted in Fig. 5 successive density curves of n,(z, t ) for the SCH and the LGRIN-SCH structures. The well is just in the middle of the z scale, the initial distribution is given by the absorption coefficient in AlGaAs which we take as 3 x lo4 cm-’ [27], and the behavior of both structures is calculated with the same set of input parameters. In the SCH, the initial population decays approximately at the same rate over the whole structure, and the finite capture time has a smaller influence on the evolution of the carrier distribution than the diffusion coefficient. In the LGRIN-SCH, the population which experiences the built-in quasi-electric field drifts to the well in less than 2 ps, and carriers have to wait above it before being trapped. The evolution of the distribution is then mainly given by the value of the quantum capture time. In Fig. 6, we compare the evolution of the carrier distribution in the LGRIN-SCH, at T = 300 K, for two different assumptions: a multivalley calculation taking into account the X valley (solid line), and a simple calculation where the photoexcited carriers only experience the I? valley quasi-field (dashed line). Note that the effect near the well (where the luminescence from the barrier is observed and calculated) is very weak. As an example, Fig. 7 shows the decay of the luminescence calculated with the two models. Photocarriers transferred from the I’ valley to the Xvalley drift in less than 1 ps down to the crossover. Note that this effect decreases for temperatures lower than 300 K. ESTIMATION OF THE MOBILITY In the SCH structure, the luminescence signal corresponds to the integral of the carrier distribution over the

IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 27. NO. 6. JUNE 1991

0

2 5 ,

100

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(a) , ,

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300

200

WELL

,

,

bo0

lnml

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150

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(b) Fig. 5 . Temporal evolution of the carrier population in the barrier layer at T = 120 K (a) for the SCH structure, (b) for the LGRIN-SCH structure. Input-parameters are D = 10 cmz . s - I , r,, = 1 ps. and capture area = 100 A for both structures.

1I

L O L ’

1

0 8

- 0 6 3

4 0 4 0 2

0

0

50

100

150 200 W E L L -Inml

250

300

Fig. 6 . Photocarrier distribution in the LGRIN-SCH for different delays after the pulse excitation. Dashed line: without multivalley calculation, full line: with multivalley calculation.

Fig. 7. Time dependence of the barrier luminescence for the LGRIN-SCH. Dashed line: with multivalley calculation, full line: without multivalley calculation.

confinement layer. The decay time then directly reflects the full diffusion process of the carriers in the barrier. In the case of the LGRIN-SCH, we only probe the carriers which are at the edge of the well. A first evaluation of the mobility has been made with the SCH (in which the diffusion coefficient is the main parameter). We have intro-

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duced a finite quantum capture time of 0.8 ps. Indeed, recent experiments made on multiple quantum owells [ 141 shows that photoexcited carriers less than 200 A from the well can be captured in a finite time of about 1 ps. We have taken this value as a reference for theoretical calculations. The values of mobility that we find are reported in Table I1 for temperatures varying from 20 to 300 K. Our mobilities seem reasonable for holes in AlGaAs [28]. Similar optical measurements have already led to an estimation of the holes' mobility in agreement with these values [29]. The smaller value of the mobility for the SCH at 20 K might be explained by the partial localization of the photoexcited carriers in alloy potential fluctuations of the confinement layers [30]. Above 50 K, the thermal energy is sufficient to overcome that localization of only a few millielectronvolts. In the GRIN-SCH structures, this kind of localization does not occur because of the quasifield experienced by the photoexcited carrier population. In the LGRIN-SCH, opposite to the case of the SCH, the decay behavior of the luminescence is mainly dependent on the value of the quantum capture time, and is not very sensitive to reasonable variations of the diffusion coefficient. As an example, we show in Fig. 8 the decay curves for an LGRIN-SCH calculated under different assumptions. It is easy to notice that the change in the capture time has a very strong influence, whereas the change in the diffusion coefficient has a much smaller effect. In Fig. 9 are shown different fits of the time-resolved luminescence from the LGRIN-SCH confinement layers at R = 120 K. The dotted curve is calculated with an instantaneous capture by the well; neither the rise nor the decay of the luminescence can be fitted (in this calculation, we used the value of the mobility obtained from the fit of the SCH behavior). The dash-dotted curve is calculated with finite quantum capture time of l ps for a layer of 100 A on each side of the well. We are then able to correctly fit the decay of the luminescence, but the theoretical curve is shifted by 1 ps with respect to the experimental curve. One of the advantages of the up-conversion technique is the very precise determination of the zero time delay (within 100 fs) [23]; this discrepancy cannot be due to an erroneous determination of the origin. An increase of the capture time does not allow us to get a better fit as it changes the slope of the decay curve before affecting the position of its maximum (see Fig. 8). In order to understand the behavior of the luminescence at short times, we have to take into account the r - L intervalley scattering, which entails a slow rise of the luminescence in GaAs at room temperature (10 ps) [24]. When excited at 2 eV, electrons in GaAs (or AIGaAs) first transfer to the L valley very rapidly. They subsequently come back to the r valley, with a characteristic time constant of 2 ps. As the mobility in the L valley is very small, this will slow down the movement of the carriers. With the input parameters taken from [24], we obtain a good fit to the experimental measurements (Fig. 9, full line). It is rather easy to obtain a consistent picture for both the SCH and the LGRIN-SCH at temperatures below 200 K. Over this temperature, it is no longer possible to get reasonable results for the LGRIN-SCH with capture times

TABLE I1 MOBILITIES DEDUCED FROM THE CALCULATIONS. BOTH THE LGRIN-SCH A N D THE SCH STRUCTURES CAN BE FITTED WITH THE SAME VALUES OF THE DIFFUSION CONSTANT (PRECISION IS ESTIMATED TO BE 50%), EXCEPT FOR T = 20 K. Temperature (K)

Mobility (cm2/V . s)

20 80 120 150 190 220 250 300

180 (SCH)/lOOO (GRIN-SCH) 1800 1230 1 loo 930 850 900 800

:-

T

*

5ps

- 1

DELAY Ips1

Fig. 8. Time decay of the carrier population in an LGRIN-SCH structure under different assumptions. All parameters are equivalent, except for the capture time and the diffusion coefficient indicated in the figure.

Fig. 9. Experimental data of the luminescence arising from the LGRIN-

SCH barrier layer at T = 120 K can be fitted by theoretical calculation with D = 10 cm2 . s - ' , r,v = 1 ps, and capture area = 100 A . Dotted line: instantaneous capture; dashed-dotted line: r,%,= 1 ps, no r-L intervalley scattering; full line: r,. = 1 ps, I'-L intervalley scattering has been introduced.

on the order of 1 ps. Two reasons may be responsible for this problem. First, the experimental data are much less precise due to thermal reemission of the carriers from the well, which slows down the observed decay time. We have tried to take this effect into account, but obviously, the deduced times are much less precise than at lower temperatures. Second, it is possible that the quantum capture time is not constant with temperature. A variation from 0.8 ps at low temperatures up to 3 ps at room temperature would explain the observed behavior. The variation with temperature of the measured times in the case of the SCH structure is a result of the variation of the diffusion coefficient: it comes from the change in the mobility together with the change in the temperature coefficient. For the case of GRIN-SCH, part of the increase in the observed times is due to the increase of the excited thickness of the sample. Following our explanation, the other part of the increase would be linked with a slight increase of the quantum capture time.

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Obviously, it appears that our classical description of the trapping process by a quantum well is better suited for an SCH structure than for an LGRIN-SCH structure in which the time of diffusion in the barrier is on the order of the quantum capture time T,,,.However, this simple phenomenological model allows us to correctly fit the temporal behavior of both structures. The behavior of the SCH at 20 K is obviously very different: it is impossible to get a fit to both the SCH and the GRIN-SCH with the same mobility. The decay of the CL luminescence for the SCH is quite long (220 ps, as also observed by Polland et al. [ 16]), and it can be explained by a very low mobility. We think that this low mobility is a result of the localization in the potential fluctuations of the alloy. This easily explains the very low capture efficiency of the SCH found by Polland et al. [16]. As soon as the temperature is raised, delocalization over these potential fluctuations occurs. and the trapping efficiency is much better. Our model differs from that of Weller et al. [25]in that we fit the decay of the barrier luminescence rather than the rise of the quantum-well luminescence, which is mainly given by cooling effects. The fit to the decay curve gives an upper limit of 180 cm2/V . s for the mobility when nonradiative lifetime is not included. If a nonradiative lifetime of 200 ps is taken into account, sych a mobility leads to a diffusion length of about 300 A (i.e., much less than the CL width), and it explains the poor capture efficiency of the SCH at 20 K. Taking a small value for the alloy mobility at low temperature seems to us more reasonable than taking a very short lifetime in the alloy (Weller et al. [25] assumed a value of 4 ps, which seems very short). VI. COMPARISON OF THE CAPTURE VELOCITY I N SCH A N D LGRINSCH STRUCTURES As we mentioned earlier, our excitation energy does not create the same initial carrier distributions in both structures, nor does the luminescence characterization that we use probe equivalent entities. In the SCH, we probe the integral of the carrier density, whereas we only probe the edge of the well in the LGRIN-SCH. However, comparison to experimental data has allowed us to adjust the parameters of the “drift-diffusion’’ model. We are now able to use this model to compare the two structures under the same (theoretical) initial conditions. We have considered two situations of interest. First, we assume an excitation energy just below the outer barrier (60%)r bandgap so that we create photoexcited carriers in the entire structure for both the SCH and the LGRIN-SCH (2000 on each side of the well). Calculations are made with the input parameters deduced from the fit to the experimental data. At T = 120 K, the decay time of the LGRIN-SCH luminescence is not changed much (2.3 ps instead of 2.2 ps). This confirms that the main limitation of the capture process is the quantum capture. At this temperature, the LGRIN-SCH is eight times faster than the SCH. At T = 300 K, in the LGRIN-SCH, the time of the drift process in the barrier becomes important compared to the quantum capture time, and the decay time of the luminescence

A

is appreciably longer (10 ps). Under such conditions, the LGRIN-SCH is only twice as fast as the SCH. Second, we have theoretically i!jected a packet of carriers at the edge of the CL (2000 A from the well) as if excitation were coming from an electrical contact. We then compared the average decay times of the carrier populations in both cases of SCH and LGRIN-SCH. The important parameter is not the slope of the decay curve (which is rather flat at the early times), but rather the time taken to decay to one tenth of its original value. At room temperature, the time computed for the SCH structure is 70 ps; it is 17.5 ps for the case of the LGRIN-SCH, i.e., four times faster. The absence of satellite valleys in InGaAs should allow even faster behavior for GRIN-SCH structures fabricated in that system compared to GaAs- AlGa As. Let us recall that, under current injection i.e., in lasing conditions for a semiconductor laser, one can assume as a first approximation that the system is under flat-band conditions. The potential shape of the structure will then be quite similar to that obtained under high optical excitation. Of course, in the case of a real laser structure, the cladding layers will be doped. Very preliminary results tend to show that a doping level of about lOI5 cm-3 leads to a negligible contribution of the impurities to the capture time [31]. VII. CONCLUSION In this paper, we have reported experimental measurements (using subpicosecond resolution) of carrier trapping in three single-quantum-well structures with different bandgap profiles of the confinement layer. We show the better suitability of GRIN-SCH structures over SCH for higher frequency modulation, even at room temperature. We have used a classical one-dimensional theoretical model to describe the temporal evolution of photoexcited carriers in the confinement layers, and mobility has been deduced from these calculations. It appears from this study that the influence of the quantum capture and the diffusion in the barrier are very dependent on the bandgap profile. In the SCH structure, the behavior of the photoexcited carrier population is found to be dominated by the diffusion of photoexcited carriers in the confinement layer, and the quantum capture only has a small effect on the “overall capture time.” In the GRIN-SCH structures, the reverse is true. At low temperature, the initial population drifts towards the well in less than 2 ps, and carriers have to wait above it before being captured. Then the quantum capture process is of great influence on the trapping time, and the diffusion constant can be reasonably varied without changing the calculated decay time of the confinement layer luminescence. At room temperature, the time of drift is large enough to have an influence on the capture process. Further experiments on GRIN-SCH’s might evidence some properties predicted from the quantum mechanical approach. It might be possible to observe resonances in the trapping time as a function of the well thickness in such structures.

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MORIN et 01.: CAPTURE OF PHOTOEXCITED CARRIERS IN SQW

ACKNOWLEDGMENT The authors are indebted to A. Chomette, B. Lambert, and A. Regreny for useful discussions, and M. Otha for his help in sample preparation. They would also like to thank P. Georges and F. Salin for their invaluable help in Setting Up the laser system, and Coherent for the loan of the double-jet dye laser.

REFERENCES J. Y. Tang, K. Hess, N. Holonyak, Jr., I. J. Coleman, and P. D. Dakpus, “The dynamics of electron-hole collection in quantum well heterostructures,” J . Appl. Phys., vol. 53, pp. 6043-6046, 1982. D. Bimberg, J . Christen, A. Steckenbom, G. Weimann, and W. Schlapp, “Injection, intersubband relaxation and recombination in GaAs multi quantum well structures,” J . Luminescence, vol. 30, pp. 562-579, 1985. B. Deveaud, T. C. Damen, J. Shah, and W. T. Tsang, “Capture of electrons and holes in quantum wells,” Appl. Phys. Len., vol. 52, pp. 1886-1888, 1988. J. Feldmann, G. Peter, E. 0. Gobel, K. Leo, H. J. Polland, K. Ploog, K. Fujiwara, and T. Nakayama, “Carrier trapping in single quantum wells with different confinement structures,’’ Appl. Phys. Lett., vol. 51, pp. 226-228, 1987. . N. Ogasawara, A. Fujiwara, N. Ohgushi, S. Fukatsu, Y.Shiraki, Y . Katayama, and R. Ito, “Well-width dependence of photoluminescence excitation spectra in GaAs/AI,Ga, - ,As quantum wells,” Phys. Rev., vol. B42, pp. 4235-4238, 1990. J. A. Brum and G. Bastard, “Resonant carrier capture by semiconductor quantum wells,” Phys. Rev., vol. B33, pp. 1420-1423. 1986. J. A. Brum, T. Weil, J. Nagle, and B. Vinter, “Calculations of carrier capture time of a quantum well in a graded index separate confinement heterostructure.” Phys. Rev., vol. B34, pp. 2381-2384, 1986. M. Babiker and B. K. Ridley, “Effective mass eigenfunctions in superlattices and their role in well capture,” Superlattice Microstructures, vol. 2, pp. 287-291, 1986. P. M. W. Blom, R. F. Mols, J. E. M. Haverkort, M. R. Leys, and J. H. Wolter, “Measurement of the ambipolar carrier capture time in a GaAs/AI,Ga, - ,As separate confinement heterostructure quantum well,” Superlattice Microstructures, vol. 7, pp. 319-323, 1990. M. Babiker, A. Ghosal, and B. K. Ridley, “Intrasubband transitions and well capture via confined guided and interface LO phonons in superlattices,” Superlattice Microstructures, vol. 5, pp. 133- 136, 1988. D.Oberli, J. Shah, J. L. Lewell, T. C. Damen, and N. Chand, “Dynamics of carrier capture in an InGaAs/GaAs quantum well trap,” Appl. Phys. Lett., vol. 54, pp. 1028-1030, 1989. R. Kersting, X . Q. Zhou, K. Wolter, D. Griitzmacher, and H. Kurz, “Subpicosecond luminescence study of carrier transfer in InGaAsl InP multiple quantum wells,’’ .Superlattice Microstructures, vol. 7, pp. 345-348, 1990. The estimation of a 300 fs capture time was based on a detection limit argument, without direct observation of the barrier luminescence [3]. With the improvement of the sensitivity of the technique, direct observation leads to longer times and to a very small intensity for the barrier luminescence [ 141. The very low intensity might be explained by the importance of the transfer to the satellite valleys. B. Deveaud, “Subpicosecond luminescence of quantum wells,” in Proc. 20th In?. Con5 Phys. Semiconductors (Thessaloniki, Greece), E. M. Anastassakis and J. D. Joannopoulos, Ed. Singapore: World Scientific, 1990, p. 1201. Kersting et al. [ 1.11, although giving slightly longer times in the case of InGaAs quantum wells, do not find a sizable change with the well thickness. The oscillations reported by Y. Shiraki et al. (Y. Shiraki, S . Fukatsu, Y. Katayama, R. Ito, A. Fujiwara, and N . Ogasawara, “Well-width dependence of carrier trapping efficiency in quantum wells,” in Proc. 20th In?. Conf. Phys. Semiconductors, E. M. Anastassakis and J. D. Joannopoulos, Ed. Singapore: World Scientific,

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S. Morin, photograph and biography not available at the time of publication.

B. Deveaud, photograph and biography not available at the time of publication.

F. Clerot, photograph and biography not available at the time of publication.

K. Fujiwara, photograph and biography not available at the time of publication.

K. Mitsunaga, photograph and biography not available at the time of publication.